If you do this, some X11 apps will automatically recognize those key functions. For example, it works in Firefox. (as of 2015-03-26, it does not work in: {Google Chrome browser, gimp, inkscape, gnome-terminal}.)

With this, all F keys work. I can now proceed to do normal keybinding in emacs or other apps with standard F keys. [see Emacs: How to Define Keys]

How to Set Keys for Linux Console?

Note: xmodmap is only for apps running under X11 (the Graphical Window system). For example, it does not change keys in Virtual Console. [see Linux: How to use Virtual Console] or linux console (the command line screen when boot up)